To solve the problem of finding the ratio of the number of grains sowed to the number harvested, let's break it down step-by-step. ### Step 1: Identify the Numbers - **Grains Sowed**: The farmer planted **5000 grains** of maize. - **Cobs Harvested**: The farmer harvested **5000 cobs**. - **Grains per Cob**: Each cob bears **500 grains**. ### Step 2: Calculate the Total Number of Grains Harvested To find the total number of grains harvested, we need to multiply the number of cobs by the number of grains per cob: \[ \text{Total Grains Harvested} = \text{Number of Cobs} \times \text{Grains per Cob} \] Substituting the values: \[ \text{Total Grains Harvested} = 5000 \text{ cobs} \times 500 \text{ grains/cob} = 2,500,000 \text{ grains} \] ### Step 3: Set Up the Ratio Now that we have both the number of grains sowed and the number harvested, we can set up the ratio: \[ \text{Ratio of Grains Sowed to Grains Harvested} = \frac{\text{Grains Sowed}}{\text{Grains Harvested}} = \frac{5000}{2,500,000} \] ### Step 4: Simplify the Ratio To simplify the ratio, we can divide both the numerator and the denominator by 5000: \[ \frac{5000 \div 5000}{2,500,000 \div 5000} = \frac{1}{500} \] Thus, the ratio of the number of grains sowed to the number harvested is: \[ 1 : 500 \] ### Step 5: Identify the Correct Option From the options provided: - A. 1 : 250,000 - B. 1 : 25,000 - C. 1 : 500 - D. 1 : 5,000 The correct answer is **C. 1 : 500**. ### Step 6: Explanation of Incorrect Options - **Option A (1 : 250,000)**: This option suggests that for every grain sown, there are 250,000 grains harvested. This is incorrect because we calculated that there are only 500 grains harvested for every grain sown. - **Option B (1 : 25,000)**: This option implies that for every grain sown, there are 25,000 grains harvested. This is also incorrect as it does not reflect the actual calculation of 500 grains harvested for each grain sown. - **Option D (1 : 5,000)**: This option suggests that for every grain sown, there are 5,000 grains harvested. This is incorrect because it underestimates the total number of grains harvested, which we calculated to be 2,500,000 grains. ### Summary - The ratio of grains sowed to grains harvested is **1 : 500**. - The total number of grains harvested is calculated by multiplying the number of cobs by the grains per cob. - Simplifying the ratio involves dividing both the numerator and denominator by the same number. - Understanding how to set up and simplify ratios is crucial for solving similar problems. ### Revision Summary - **Grains Sowed**: 5000 grains. - **Total Grains Harvested**: 5000 cobs × 500 grains/cob = 2,500,000 grains. - **Ratio Calculation**: 5000 grains sowed to 2,500,000 grains harvested simplifies to 1 : 500. - **Correct Option**: C. 1 : 500.